Solve Linear Equations worksheet with multiple algebraic problems for practice.

Let's solve each of the linear equations step by step.

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1. $ 3x - 20 + 2x = 10 $

Step 1: Combine like terms on the left side:
$ (3x + 2x) - 20 = 10 $ → $ 5x - 20 = 10 $

Step 2: Add 20 to both sides:
$ 5x = 30 $

Step 3: Divide by 5:
$ x = 6 $

✔ Answer: $ x = 6 $

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2. $ -x - 5 + 3x = 3 $

Step 1: Combine like terms:
$ (-x + 3x) - 5 = 3 $ → $ 2x - 5 = 3 $

Step 2: Add 5 to both sides:
$ 2x = 8 $

Step 3: Divide by 2:
$ x = 4 $

✔ Answer: $ x = 4 $

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3. $ x - 8 + 2x = 7 $

Step 1: Combine like terms:
$ (x + 2x) - 8 = 7 $ → $ 3x - 8 = 7 $

Step 2: Add 8 to both sides:
$ 3x = 15 $

Step 3: Divide by 3:
$ x = 5 $

✔ Answer: $ x = 5 $

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4. $ -6 - x + 3x = 2 $

Step 1: Combine like terms:
$ -6 + (-x + 3x) = 2 $ → $ -6 + 2x = 2 $

Step 2: Add 6 to both sides:
$ 2x = 8 $

Step 3: Divide by 2:
$ x = 4 $

✔ Answer: $ x = 4 $

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5. $ -5 + 3x + x = 7 $

Step 1: Combine like terms:
$ -5 + (3x + x) = 7 $ → $ -5 + 4x = 7 $

Step 2: Add 5 to both sides:
$ 4x = 12 $

Step 3: Divide by 4:
$ x = 3 $

✔ Answer: $ x = 3 $

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6. $ -2 + 3x - 2x = 4 $

Step 1: Combine like terms:
$ -2 + (3x - 2x) = 4 $ → $ -2 + x = 4 $

Step 2: Add 2 to both sides:
$ x = 6 $

✔ Answer: $ x = 6 $

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7. $ 3x - 7 + 2x = 18 $

Step 1: Combine like terms:
$ (3x + 2x) - 7 = 18 $ → $ 5x - 7 = 18 $

Step 2: Add 7 to both sides:
$ 5x = 25 $

Step 3: Divide by 5:
$ x = 5 $

✔ Answer: $ x = 5 $

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8. $ -16 + x + 3x = 8 $

Step 1: Combine like terms:
$ -16 + (x + 3x) = 8 $ → $ -16 + 4x = 8 $

Step 2: Add 16 to both sides:
$ 4x = 24 $

Step 3: Divide by 4:
$ x = 6 $

✔ Answer: $ x = 6 $

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9. $ -2 + x + 2x = 7 $

Step 1: Combine like terms:
$ -2 + (x + 2x) = 7 $ → $ -2 + 3x = 7 $

Step 2: Add 2 to both sides:
$ 3x = 9 $

Step 3: Divide by 3:
$ x = 3 $

✔ Answer: $ x = 3 $

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10. $ -x - 3 + 2x = 3 $

Step 1: Combine like terms:
$ (-x + 2x) - 3 = 3 $ → $ x - 3 = 3 $

Step 2: Add 3 to both sides:
$ x = 6 $

✔ Answer: $ x = 6 $

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✔ Final Answers:

| Equation | Solution |
|--------|---------|
| $ 3x - 20 + 2x = 10 $ | $ x = 6 $ |
| $ -x - 5 + 3x = 3 $ | $ x = 4 $ |
| $ x - 8 + 2x = 7 $ | $ x = 5 $ |
| $ -6 - x + 3x = 2 $ | $ x = 4 $ |
| $ -5 + 3x + x = 7 $ | $ x = 3 $ |
| $ -2 + 3x - 2x = 4 $ | $ x = 6 $ |
| $ 3x - 7 + 2x = 18 $ | $ x = 5 $ |
| $ -16 + x + 3x = 8 $ | $ x = 6 $ |
| $ -2 + x + 2x = 7 $ | $ x = 3 $ |
| $ -x - 3 + 2x = 3 $ | $ x = 6 $ |

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